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visits member for 3 years, 11 months
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2d
answered binomial/factorial identity mod p
2d
answered Subsets of $\mathbb{N}$ whose lower density respects complements
Jun
21
comment Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
(...) a negative answer to one of the (open) questions posed in the final section of arxiv.org/abs/1506.04664 (namely, Question 6), provided we work, e.g., in a model of ZF where at least two measures with the above characteristics exist. As a matter of fact, we don't know whether the answer to the same question is negative in an arbitrary model of ZF.
Jun
20
revised Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
Made $\mu^\ast$ into a nonnegative function
Jun
20
comment Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
Just came to my mind that every nonnegative additive measure on an algebra of sets is monotone, so I removed the word "monotone" from both the body and the title of the question.
Jun
20
comment Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
I was hoping for your answer, Martin. I mentioned this thread to Georges Grekos, and he commented something like: "Since you put it in MO, Martin Sleziak will answer..." :-) Thank you so much! I must confess that I've had a hard time reading van Douwen's paper, and stopped just at Section 5, as it wasn't, and isn't yet, clear to me whether Constructions 5.2 and 5.3 in that very section give rise to different measures or not. The reason why I was so interested is that having more than one additive measure on ${\bf N}^+$ with the rigidity properties specified in the OP yields (...)
Jun
20
revised Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
Removed any reference to monotonicity from the body of the OP and the title
Jun
20
accepted Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
Jun
19
comment Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
A "similar" question was picked up here: mathoverflow.net/questions/27989.
Jun
19
comment Does there exist $k\ge2$ s.t. $X \subseteq \mathbf N^+$ has positive upper Banach density if the counting function of $X$ is $\gg n/\log^{[k]}(n)$?
Yes, and I was thinking of cancelling the post after having discussed the question with Alain Plagne. Should I? I see now the idea I had in mind can't work in any case.
Jun
19
revised Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
Clarified the question
Jun
19
revised Does there exist $k\ge2$ s.t. $X \subseteq \mathbf N^+$ has positive upper Banach density if the counting function of $X$ is $\gg n/\log^{[k]}(n)$?
Fixed typo in the title
Jun
19
revised Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
added 242 characters in body
Jun
19
asked Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$
Jun
19
revised Does there exist $k\ge2$ s.t. $X \subseteq \mathbf N^+$ has positive upper Banach density if the counting function of $X$ is $\gg n/\log^{[k]}(n)$?
Removed a useless assumption
Jun
19
revised Does there exist $k\ge2$ s.t. $X \subseteq \mathbf N^+$ has positive upper Banach density if the counting function of $X$ is $\gg n/\log^{[k]}(n)$?
added 19 characters in body
Jun
19
asked Does there exist $k\ge2$ s.t. $X \subseteq \mathbf N^+$ has positive upper Banach density if the counting function of $X$ is $\gg n/\log^{[k]}(n)$?
Jun
18
comment Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property
No problem, I think it's enough to record it in a comment.
Jun
16
revised Sums of two squares: positive lower density?
Fixed a wrong reference
Jun
16
revised Who needs a symmetric upper asymptotic density on the integers?
Fixed a typo